On each trial of a digit span memory task, the participant is asked to read aloud a string of random digits. The participant must then repeat the digits in the correct order. If the participant is successful, the length of the next string is increased by one. For instance, if the participant repeats four digits successfully, she will hear five random digits on the next trial. The participant's score is the longest string of digits she can successfully repeat. A professor of cognitive psychology is interested in the number of digits successfully repeated on the digit span task among college students. She measures the number of digits successfully repeated for 49 randomly selected students. The professor knows that the distribution of scores is normal, but she does not know that the true average number of digits successfully repeated on the đigt span task among college students is 7.06 đigits with a standard deviation of 1.63 digits. The expected value of the mean of the 49 randomly selected students, M, is - (Hint: Use the population mean and/or standard deviation just given to calculate the expected value of M.) The standard error of Mis - (Hint: Use the population mean and/or standard deviation just given to calculate the standard error.) The Dataview tool that follows displays a data set consisting of 200 potential samples (each sample has 49 observations). Data Set Samples Sample arabies -2 Oenations - 200 statistics for 200 Random Samples (n = 49) drawn from a normal distribution of Digit span Scores Rwas used to generate the samples. Cbsarvations Varable Form A h a sanA Sampie ears artitate Numerie 200 Sampie Qaritate Numere 200 Variable Variable Correlation Correlation

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On each trial of a digit span memory task, the participant is asked to read aloud a string of random digits. The participant must then repeat the digits
in the correct order. If the participant is successful, the length of the next string is increased by one. For instance, if the participant repeats four digits
successfully, she will hear five random digits on the next trial. The participant's score is the longest string of digits she can successfully repeat.
A professor of cognitive psychology is interested in the number of digits successfully repeated on the digit span task among college students. She
measures the number of digits successfully repeated for 49 randomly selected students. The professor knows that the distribution
scores is normal.
but she does not know that the true average number of digits successfully repeated on the digit span task among college students is 7.06 digits with a
standard deviation of 1.63 digits.
The expected value of the mean of the 49 randomly selected students, M, is v
(Hint: Use the population mean and/or standard deviation just
given to calculate the expected value of M.)
The standard error of Mis
(Hint: Use the population mean and/or standard deviation just given to calculate the standard error.)
The DataView tool that follows displays a data set consisting of 200 potential samples (each sample has 49 observations).
Data Set
Samples
Sample
Variables - 2
Observations - 200
Statistics for 200 Random Samples (n = 49) drawn from a normal distribution of Digit Span
Scores
Rwas used to generate the samples.
Variables
Observations
Туре
Observations>
Varlable V
Form V
Values V
Missing V
Sample Means
Quantitative
Numeric
200
Sample SD
Quantitative
Numeric
200
Varlable
Varlable
Correlation
Correlation
Suppose this professor happens to select Sample 133. (Hint: To see a particular sample, click the Observations button on the left-hand side of the
Transcribed Image Text:On each trial of a digit span memory task, the participant is asked to read aloud a string of random digits. The participant must then repeat the digits in the correct order. If the participant is successful, the length of the next string is increased by one. For instance, if the participant repeats four digits successfully, she will hear five random digits on the next trial. The participant's score is the longest string of digits she can successfully repeat. A professor of cognitive psychology is interested in the number of digits successfully repeated on the digit span task among college students. She measures the number of digits successfully repeated for 49 randomly selected students. The professor knows that the distribution scores is normal. but she does not know that the true average number of digits successfully repeated on the digit span task among college students is 7.06 digits with a standard deviation of 1.63 digits. The expected value of the mean of the 49 randomly selected students, M, is v (Hint: Use the population mean and/or standard deviation just given to calculate the expected value of M.) The standard error of Mis (Hint: Use the population mean and/or standard deviation just given to calculate the standard error.) The DataView tool that follows displays a data set consisting of 200 potential samples (each sample has 49 observations). Data Set Samples Sample Variables - 2 Observations - 200 Statistics for 200 Random Samples (n = 49) drawn from a normal distribution of Digit Span Scores Rwas used to generate the samples. Variables Observations Туре Observations> Varlable V Form V Values V Missing V Sample Means Quantitative Numeric 200 Sample SD Quantitative Numeric 200 Varlable Varlable Correlation Correlation Suppose this professor happens to select Sample 133. (Hint: To see a particular sample, click the Observations button on the left-hand side of the
Suppose this professor happens to select Sample 133. (Hint: To see a particular sample, click the Observations button on the left-hand side of the
DataView tool. The samples are numbered in the first column, and you can use the scroll bar on the right side to scroll to the sample you want.)
Use the DataView tool to find the mean and the standard deviation for Sample 133. The mean for Sample 133 is
The standard deviation
for Sample 133 is v
Using the distribution of sample means, calculate the z-score corresponding to the mean of Sample 133. The z-score corresponding to the mean of
Sample 133 is
Use the Distributions tool that follows to determine the probability of obtaining a mean number of digits successfully repeated greater than the mean
of Sample 133.
Standard Normal Distribution
Sendere Cevtent0
-3
-1
3
The probability of obtaining a sample mean greater than the mean of Sample 133 is
If the sample you select for your statistical study is 1 of the 200 samples you drew in your repeated sampling, the worst-luck sample you could draw is
(Hint: The worst-luck sample is the sample whose mean is farthest from the true mean. You may find it helpful to sort the
sample means: In Observations view dick the arrow below the column heading Sample Means.)
Transcribed Image Text:Suppose this professor happens to select Sample 133. (Hint: To see a particular sample, click the Observations button on the left-hand side of the DataView tool. The samples are numbered in the first column, and you can use the scroll bar on the right side to scroll to the sample you want.) Use the DataView tool to find the mean and the standard deviation for Sample 133. The mean for Sample 133 is The standard deviation for Sample 133 is v Using the distribution of sample means, calculate the z-score corresponding to the mean of Sample 133. The z-score corresponding to the mean of Sample 133 is Use the Distributions tool that follows to determine the probability of obtaining a mean number of digits successfully repeated greater than the mean of Sample 133. Standard Normal Distribution Sendere Cevtent0 -3 -1 3 The probability of obtaining a sample mean greater than the mean of Sample 133 is If the sample you select for your statistical study is 1 of the 200 samples you drew in your repeated sampling, the worst-luck sample you could draw is (Hint: The worst-luck sample is the sample whose mean is farthest from the true mean. You may find it helpful to sort the sample means: In Observations view dick the arrow below the column heading Sample Means.)
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